1/ln(x)*e^(1/x)
if you differentiate e^(1/x), you will get ln(x)*e^(1/x). times this by 1/ln(x) and you get you original equation. Peace
Powers of e are simple to integrate. The derivative of eu equals u'eu; inversely, the antiderivative of eu equals eu/u'. Therefore, the antiderivative of e1/-x equals (e1/-x)/{d/dx[1/-x]}. The derivative of 1/-x, which can also be expressed as x-1, equals (-1)x(-1-1) = -x-2 = -1/x2.
The antiderivative of 1/x is ln(x) + C. That is, to the natural (base-e) logarithm, you can add any constant, and still have an antiderivative. For example, ln(x) + 5. These are the only antiderivatives; there are no different functions that have the same derivatives. This is valid, in general, for all antiderivatives: if you have one antiderivative of a function, all other antiderivatives are obtained by adding a constant.
int(e 3x) = (1/3)e 3x ========
if you mean e to the x power times log of x, it is e to the x divided by x
one.
Powers of e are simple to integrate. The derivative of eu equals u'eu; inversely, the antiderivative of eu equals eu/u'. Therefore, the antiderivative of e1/-x equals (e1/-x)/{d/dx[1/-x]}. The derivative of 1/-x, which can also be expressed as x-1, equals (-1)x(-1-1) = -x-2 = -1/x2.
The antiderivative, or indefinite integral, of ex, is ex + C.
-e-x + C.
One can use integration by parts to solve this. The answer is (x-1)e^x.
The antiderivative of 1/x is ln(x) + C. That is, to the natural (base-e) logarithm, you can add any constant, and still have an antiderivative. For example, ln(x) + 5. These are the only antiderivatives; there are no different functions that have the same derivatives. This is valid, in general, for all antiderivatives: if you have one antiderivative of a function, all other antiderivatives are obtained by adding a constant.
int(e 3x) = (1/3)e 3x ========
The integral would be 10e(1/10)x+c
Power is energy divided by time, P=E/t.
You gave no examples to choose from. Power is Energy divided by time. P = E/t In the metric system, the unit of power is the Watt. One Watt is one Joule per second, energy divided by time, 1 J/s. Power is the rate of change of energy.
if you mean e to the x power times log of x, it is e to the x divided by x
James E. Preston has written: 'One world divided'
No, power is the rate at which work is done or energy is transferred. It is calculated by dividing work by time. Power = Work / Time.